Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 4.7, Problem 3PT
To determine
To choose: The appropriate option for maximum area for the function of triangular area in terms of x that is used to find the maximum area.
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3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 4 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 4.1 - Prob. 1PTCh. 4.1 - Sometimes, Always, or Never: If f(c) = 0, then c...Ch. 4.1 - The critical numbers of f(x) = 3x4 = 20x3 36x2...Ch. 4.1 - Prob. 4PTCh. 4.1 - True or False: The absolute extrema of a...Ch. 4.1 - Prob. 6PTCh. 4.1 - Prob. 7PTCh. 4.2 - Prob. 1PTCh. 4.2 - Prob. 2PTCh. 4.2 - Prob. 3PT
Ch. 4.2 - True or False: If f(x) = g(x) for all x then f(x)...Ch. 4.2 - Prob. 5PTCh. 4.3 - Prob. 1PTCh. 4.3 - Prob. 2PTCh. 4.3 - Prob. 3PTCh. 4.3 - Prob. 4PTCh. 4.3 - Prob. 5PTCh. 4.3 - Prob. 6PTCh. 4.3 - True or False: If f(c) = 0, then c is a point of...Ch. 4.3 - Prob. 8PTCh. 4.3 - Prob. 9PTCh. 4.3 - Prob. 10PTCh. 4.4 - Prob. 1PTCh. 4.4 - Prob. 2PTCh. 4.4 - Prob. 3PTCh. 4.4 - limx(lnx)1/x= a) 0 b) 1 c) e d)Ch. 4.5 - Prob. 1PTCh. 4.5 - Prob. 2PTCh. 4.5 - Prob. 3PTCh. 4.5 - True or False: If f(x) 0 for all x in an interval...Ch. 4.5 - Prob. 5PTCh. 4.5 - Prob. 6PTCh. 4.5 - Prob. 7PTCh. 4.6 - Prob. 1PTCh. 4.6 - Prob. 2PTCh. 4.6 - Prob. 3PTCh. 4.7 - Prob. 1PTCh. 4.7 - A carpenter has a 10-foot-long board to mark off a...Ch. 4.7 - Prob. 3PTCh. 4.7 - Prob. 4PTCh. 4.8 - Prob. 1PTCh. 4.8 - Prob. 2PTCh. 4.8 - Prob. 3PTCh. 4.9 - Prob. 1PTCh. 4.9 - Prob. 2PTCh. 4.9 - Prob. 3PTCh. 4.9 - Prob. 4PTCh. 4.9 - Prob. 5PT
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- Question 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .arrow_forwardanswerarrow_forward
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